| Boiling and natural convection processes in a fluid-saturated porous medium are investigated. The purpose of the investigation is to provide a theoretical basis to previous experimental studies. The porous medium is heated from below or volumetrically, and cooled from above. The thermodynamic structure consists of a two-phase region at the bottom, and a liquid region at the top. Analytical and numerical methods are used to solve the equations in the two regions. The parameters in the equations are: Rayleigh number (R), bottom heat flux ({dollar}Qsb{lcub}b{rcub}{dollar}), volumetric heating rate ({dollar}Qsb{lcub}i{rcub}{dollar}) and aspect ratio of the porous bed (AR).; A linear stability analysis is carried out for a horizontally unbounded porous layer heated from below. It is found that the critical Rayleigh number for onset of convection is lowered by the presence of a two-phase region. The convective instability is produced by buoyancy as well as phase change effects. The flow field at marginal stability indicates that the liquid region streamlines penetrate the two-phase region. In the limit as R {dollar}rightarrow{dollar} O, a two layer structure (liquid overlying two-phase) with a liquid-dominated two-phase region is unconditionally stable. However, a two layer structure with a vapor-dominated two-phase region is stable only below a critical permeability value. The analysis is extended to a finite 3-D porous box, and preferred convective modes are obtained. The various heat transfer regimes for bottom heated beds are also discussed.; A numerical study is carried out in a rectangular porous bed. A novel numerical scheme which uses finite differences on a deformable grid is devised and implemented. A parametric study is carried out for bottom heated beds in the R {dollar}-{dollar} {dollar}Qsb{lcub}b{rcub}{dollar} space. Three solutions regimes are observed: conduction dominated at low R, convection dominated at higher R, and oscillatory convection at high R. In the convection dominated regime, transitions to multiple cell patterns are possible as {dollar}Qsb{lcub}b{rcub}{dollar} is increased. Oscillatory convection is triggered by asymmetric disturbances in the solution. The oscillations are characterized by periodic transitions between cell patterns. The solutions at large {dollar}Qsb{lcub}b{rcub}{dollar} show a dependence on the initial conditions. The qualitative flow patterns and heat transfer correlations are in excellent agreement with experiments. Similar solutions are observed for volumetrically heated porous beds. |
